
generalise the ones in [1]}, [2]} because those results were originally designed for a single equation, meaning that we really need a generalisation to systems. Moreover, differently from what was done in [1]}, [2]}, we do not request that the solution of (REF ) vanish on an open set of its domain. In particular, one of our assumptions is the existence of a \(C^1\)  function \(t\mapsto v(t)\)  such that \(u\)  agrees with \(v\)  on an open set.

extend the previous ones because our approach does not preclude the case \(\rho =0\) . If this happens, we return to the CH equation and, according to the observation above, we do not use a strong premise such that \(u\)  vanishes on an open set, like was done [1]}, [2]}, although we do not necessarily avoid this possibility. Therefore, in case \(\rho =0\)  and the function \(v(\cdot )\)  mentioned above vanishes, then we return to the conditions required in [2]}, [1]}.

